Received March 3, 2022. Published online January 17, 2023.
Abstract: We study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring $R$ satisfies McCoy's theorem of skew Hurwitz series.
Keywords: skew Hurwitz series ring; $\omega$-compatible ring; skew Hurwitz serieswise; quasi-Armendariz rings; zip ring; APP ring
Affiliations: Rajendra Kumar Sharma, Department of Mathematics, Indian Institute of Technology, New Delhi-110016, India, e-mail: rksharmaiitd@gmail.com; Amit B. Singh (corresponding author), Department of Computer Science and Engineering, Jamia Hamdard (deemed to be University), New Delhi-110062, India, e-mail: amit.bhooshan84@gmail.com